It is a well-known fact that decimation of a signal without corresponding filtering, e.g. anti-aliasing or low-pass filtering, may cause the decimated signal to be distorted or otherwise damaged.
Conventional FIR-filtering is usually performed by convolving a finite number of impulse response coefficients h[k] of a desired FIR-filter with an equivalent number of samples from the input signal x[n] in order to establish one sample of the output signal y[n]:
            y      ⁡              [        n        ]              =                            h          ⁡                      [            k            ]                          *                  x          ⁡                      [            n            ]                              =                        ∑                      k            =            0                                N            -            1                          ⁢                  (                                    h              ⁡                              [                k                ]                                      ·                          x              ⁡                              [                                  n                  -                  k                                ]                                              )                      ,where N is the length of the impulse response h[n].
Thus, for each output sample, N multiplications and N−1 additions have to be made. For practically all signal processors multiplications form a bottleneck and with a FIR filter having a resolution of, e.g., 384 coefficients, i.e. an N of 384, this results in 384 multiplications per sample. When the sample rate of the input signal is high, e.g. 200 MHz and the filtering is performed on each sample these 384 multiplications should be carried out within less than 5 nanoseconds. This is practically impossible or requires at least extremely expensive and demanding signal processing means. Also, when the FIR filter to be applied is very complex, e.g. having thousands of coefficients or very high-precision coefficient values it may be almost impossible or at least require excessive processing power
It is an object of the present invention to provide a method for applying a filter to a signal in such a way that less processing power or time is needed for the filtering, e.g. for use with signals of a relatively high frequency, e.g. 200 MHz, or for relatively advanced filters.
It is a further object of the present invention to provide the option of decimating the signal rate to a lower frequency, e.g. 1.5 MHz or 384 kHz.